Uniaxial symmetric FGM I-beam combination torsion based on the"plate beam theory"
At present,there is relatively little research on functional gradient materials(FGM)I-section beams as the research object.Based on Professor ZHANG Wenfu's"plate beam theory",this paper focuses on the composite torsion theory of I-section beams with rectangular solid and uniaxial symmetry as the object.Based on the"plate beam theory",the total strain energy equation was derived to obtain the flexural stiffness and free torsional stiffness of the beam.Then,the total potential energy expression was gradually derived through the external force potential energy formula and the total strain energy formula.On this basis,using the energy variational model and differential equation model,combined with boundary conditions,the calculation formula for the maximum torsion angle at the end of the beam was derived.The calculated maximum torsion angle was then compared with the finite element model results established by ANSYS.The minimum error was 0.01％and the maximum error was 1.85％.The expression for the combined torsional total strain energy of a rectangular solid single axis symmetric I-beam with a wing edge along the width variation of FGM was derived.The expressions for the torsional angle and maximum torsional angle under one end fixed and one end free boundary conditions were given,further verifying the correctness of the"plate beam theory".
functionally gradient materialscombined torsionplate beam theoryfinite element analysis
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